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If the discriminant is a perfect square then the answer is this?
Wiki User
∙ 14y ago
If the discriminant is a perfect square, it makes calculation easy on paper. Otherwise, the only property of the discriminant that matters is whether it is positive, negative or zero.
Wiki User
∙ 14y ago
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Is 9x2-36x 16 a perfect square trinomial?
If you mean: 9x2-36x+16 then it is not a perfect square because its discriminant is greater than zero
When the discriminant is a perfect square are the solutions rational or irrational?
The "discriminant" here refers to the part of the quadratic equation under the radical (square root) sign. When it is a perfect square, the square root is also a perfect square, so the radical goes away, leaving only rational numbers. So, when the discriminant is a perfect square, the solutions are (usually) rational. Unless, of course, some other part of the result is irrational. For example, if the coefficient of the x2 term ("a" in the quadratic formula) is pi, and the constant term is 1/pi, the discriminant will turn out to be 4 (4ac = 4 * pi * 1/pi = 4), which is a perfect square, but solutions will be irrational anyway because the denominator becomes 2pi, and pi is irrational.
81x2 - 72x plus 16 is a perfect square trinomial true or false?
If a trinomial is a perfect square, then the discriminant will equal 0. The discriminant is equal to B^2-4AC. The variables come from the standard form of a quadratic which is Ax^2+Bx+C In this problem, A=81, B=-72, and C=16 so the discriminant is: (-72)^2-4(81)(16)=5,184-5,184=0 so this is a perfect square trinomial. To factor, notice that 81=9^2 and 16=4^2, so 81x^2=(9x)^2. We can then factor the trinomial into (9x+4)(9x-4)
Can 9x²-24x 16 be factored using the perfect square?
If you mean 9x^2-24x+16 then yes it can because its discriminant is equal to zero and it is (3x-4)(3x-4) when factored
What is the discriminant in a math equation?
In a quadratic equation of the form ax2+bx + c = 0, the discriminant is b2-4ac. It determines the nature of the roots of the equation. If it is positive, there are two real roots; if is negative, there are two complex roots; if it is zero, there is one real root, often called a double root. Both real roots are rational if and only the discriminant is a perfect square.
When the discriminant is perfect square the answer to a quadratic equation will be?
Rational.
What does the discriminant have to be in order for the roots of a quadratic to be irrational?
The discriminant must be a positive number which is not a perfect square.
What is true of the discriminant when the two real number solutions to a quadratic equation are rational numbers?
The discriminant must be a perfect square or a square of a rational number.
Is 9x2-36x 16 a perfect square trinomial?
If you mean: 9x2-36x+16 then it is not a perfect square because its discriminant is greater than zero
When the discriminant is a perfect square are the solutions rational or irrational?
The "discriminant" here refers to the part of the quadratic equation under the radical (square root) sign. When it is a perfect square, the square root is also a perfect square, so the radical goes away, leaving only rational numbers. So, when the discriminant is a perfect square, the solutions are (usually) rational. Unless, of course, some other part of the result is irrational. For example, if the coefficient of the x2 term ("a" in the quadratic formula) is pi, and the constant term is 1/pi, the discriminant will turn out to be 4 (4ac = 4 * pi * 1/pi = 4), which is a perfect square, but solutions will be irrational anyway because the denominator becomes 2pi, and pi is irrational.
Is 4x squared plus 20x plus 25 a perfect square trinomial?
Yes because its discriminant is equal to zero
What is true of the disciminant when the two real numbers solutions to a quadratic equation are irrational numbers?
In that case, the discriminant is not a perfect square.
Why the discriminant of a quadratic is useful in algebra?
Because the square root of the discriminant is a component of the roots of the equation.
81x2 - 72x plus 16 is a perfect square trinomial true or false?
If a trinomial is a perfect square, then the discriminant will equal 0. The discriminant is equal to B^2-4AC. The variables come from the standard form of a quadratic which is Ax^2+Bx+C In this problem, A=81, B=-72, and C=16 so the discriminant is: (-72)^2-4(81)(16)=5,184-5,184=0 so this is a perfect square trinomial. To factor, notice that 81=9^2 and 16=4^2, so 81x^2=(9x)^2. We can then factor the trinomial into (9x+4)(9x-4)
Which of the folllowing indicates that the roots of a quadratic are irrational?
The discriminant is the expression inside the square root of the quadratic formula. For a quadratic ax² + bx + c = 0, the quadratic formula is x = (-b +- Sqrt(b² - 4ac))/(2a). The expression (b² - 4ac) is the discriminant. This can tell a lot about the type of roots. First, if the discriminant is a negative number, then it will have two complex roots. Because you have a real number plus sqrt(negative) and real number minus sqrt(negative). You asked about irrational. If the discrimiant is a perfect square number {like 1, 4, 9, 16, etc.} then the quadratic will have two distinct rational roots (which are real numbers). If the discriminant is zero, then you will have a double root, which is a real rational number. So if the discrimiant is positive, but not a perfect square, then the roots will be irrational real numbers. If the discriminant is a negative number which is not the negative of a perfect square, then imaginary portion of the complex number will be irrational.
How can you determine if a general quadratic trinomial is factorable?
If the quadratic is written in the form ax2 + bx + c (where a not 0) then for it to be factorable, b2 - 4ac (the discriminant) must be a perfect square.
What is a discriminant and how does help to solve equations?
In the quadratic formula, the discriminant is b2-4ac. If the discriminant is positive, the equation has two real solutions. If it equals zero, the equation has one real solution. If the discriminant is negative, it has two imaginary solutions. This is because you find the square root of the discriminant and add or subtract it from -b and divide the sum or difference by 2a. If the square root is of a positive number, then you get two different solutions, one from adding the discriminant to -b and one from subtracting the discriminant from -b. If the square root is of zero, then it equals zero, and the solution is -b/2a. If the square root is of a negative number, then you have two imaginary solutions because you can't take the square root of a negative number and get a real number. One solution is from subtracting the discriminant from -b and dividing by 2a, and the other is from adding it to -b and dividing by 2a. The parabola on the left has a positive discriminant. The parabola in the middle has a discriminant of zero. The parabola on the right has a negative discriminant.
